it has been proved that sphericity testing for digraphs is an np-complete problem. here, we investigate sphericity of 3-connected single source digraphs. we provide a new combinatorial characterization of sphericity and give a linear time algorithm for sphericity testing. our algorithm tests whether a 3-connected single source digraph with $n$ vertices is spherical in $o(n)$ time.

We give a new proof of version the main theorem previous paper in series about embedding an algebraic system into ultraproducts.

We begin by studying certain semigroup estimates which are more singular than those implied by a Sobolev embedding theorem but which are equivalent to certain logarithmic Sobolev inequalities. We then give a method for proving that such log–Sobolev inequalities hold for Euclidean regions which satisfy a particular Hardy–type inequality. Our main application is to show that domains which have ex...

1. Interpolation inequalities. A classical problem in analysis is to understand how “smoothness” controls norms that measure the “size” of functions. Maz’ya recognized in his classic text on Sobolev spaces the intrinsic importance of inequalities that would refine both Hardy’s inequality and Sobolev embedding. Dilation invariance and group symmetry play an essential role in determining sharp co...

Dedukti has been proposed as a universal proof checker. It is a logical framework based on the λΠcalculus modulo that is used as a backend to verify proofs coming from theorem provers, especially those implementing some form of rewriting. We present a shallow embedding into Dedukti of proofs produced by Zenon Modulo, an extension of the tableau-based first-order theorem prover Zenon to deductio...

The Main Theorem of this article asserts in part that if an extension V ⊆ V satisfies the δ approximation and covering properties, then every embedding j : V → N definable in V with critical point above δ is the lift of an embedding j ↾ V : V → N definable in the ground model V . It follows that in such extensions there can be no new weakly compact cardinals, totally indescribable cardinals, st...

In this paper, the necessary embedding dimension for electroencephologram(EEG) data is calculated. The tools used include a 1981 theorem from Floris Takens, and a subsequent extension of that theorem in 1991 given by Casdagli, Sauer and Yorke. These theorems give a method of reconstructing the phase space of the original system up to diffeomorphism using time-delays. If d is the original dimens...

We give an overview of Tutte’s paper, “How to draw a graph”, that contains: (i) a proof that every simple 3-connected planar graph admits a straight-line embedding in the plane such that each face boundary is a convex polygon, (ii) an elegant algorithm for finding such an embedding, (iii) an algorithm for testing planarity, and (iv) a proof of Kuratowski’s theorem.

We discuss a proof of the wellfounded induction theorem for the ordinals up to ε0. The proof is performed on the embedding of ACL2 in HOL-4, thus providing logical justification for that embedding and supporting the claim that the ACL2 logic has a model.